Scale invariant energy smoothing estimates for the Schrödinger equation with small magnetic potential

Article type: Research Article

Authors: Georgiev, Vladimir | Tarulli, Mirko

Affiliations: Dipartimento di Matematica, Università degli Studi di Pisa, Largo Bruno Pontecorvo 5, 56127 Pisa, Italy

Abstract: We consider some scale invariant generalizations of the smoothing estimates for the free Schrödinger equation obtained by Kenig, Ponce and Vega (Ann. Inst. H. Poincaré Anal. Non Lineaire 10(3) (1993), 255–288; Invent. Math. 134(3) (1998), 489–545). Applying these estimates and using appropriate commutator estimates, we obtain similar scale invariant smoothing estimates for perturbed Schrödinger equation with small magnetic potential.

Keywords: Schrödinger equation, smoothing estimates, magnetic potential

Journal: Asymptotic Analysis, vol. 47, no. 1-2, pp. 107-138, 2006